Weighted Shapley hierarchy levels values

Abstract

In this paper we present a new class of values for cooperative games with level structure.
We use a multi-step proceeding, suggested first in Owen (1977), applied to the weighted
Shapley values. Our first axiomatization is an generalisation of the axiomatization given
in Gómez-Rúa and Vidal-Puga (2011), itselves an extension of a special case of an axiomatization given in Myerson (1980) and Hart and Mas-Colell (1989) respectively by
efficiency and weighted balanced contributions. The second axiomatization is completely
new and extends the axiomatization of the weighted Shapley values introduced in Hart
and Mas-Colell (1989) by weighted standardness for two player games and consistency.
As a corollary we obtain a new axiomatization of the Shapley levels value.